MI Preprints

Title:A dynamic programming algorithm for optimizing baseball strategies
Author : Akifumi Kira, Keisuke Inakawa, Toshiharu Fujita & Kotaro Ohori
Abstract: In this paper, baseball is formulated as a finite Markov game with approximately 6.45 million states. We give an effective dynamic programming algorithm which computes Markov perfect equilibria and the value functions of the game for both teams in 2 second per game. Optimal decision making can be found depending on the situation---for example, for the batting team, whether batting for a hit, stealing a base or sacrifice bunting will maximize their win percentage, or for the fielding team, whether to pitch to or intentionally walk a batter, yields optimal results. In addition, our algorithm makes it possible to compute the optimal batting order, in consideration of strategy optimization such as a sacrifice bunt or a stolen base. The authors believe that this baseball model is also useful as a benchmark instance for evaluating the performances of (multi-agent) Reinforcement Learning methods.

File: 2015-10pdf

Title:Traveling waves bifurcating from plane Poiseuille flow of the compressible Navier-Stokes equation
Author : Yoshiyuki Kagei & Takaaki Nishida
Abstract: Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number $\rm R$ and Mach number $\rm M$ are sufficiently small. On the other hand, for $\rm R$ and $\rm M$ being not necessarily small, an instability criterion for plane Poiseuille flow is known; and the criterion says that, when $\rm R$ increases, a pair of complex conjugate eigenvalues of the linearized operator cross the imaginary axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the imaginary axis.

File: 2015-9pdf

Title:Stability of time periodic solution of the Navier-Stokes equation on the half-space under oscillatory moving boundary condition
Author : Yoshiyuki Kagei & Ryouta Oomachi
Abstract: Navier-Stokes system on the half space with periodically oscillating boundary has a time periodic solution which depends on time variable and vertical variable only. It is proved that the time periodic solution is asymptotically stable when the Reynolds number is sufficiently small; and the decay estimates of the perturbations are established in the frameworks of both strong and weak solutions.

File: 2015-8pdf

Title:Quasi-Bayesian model comparison for LAQ models
Author : Shoichi Eguchi & Hiroki Masuda
Abstract: We will prove a general result about the stochastic expansion of the logarithmic marginal quasi-likelihood associated with a class of locally asymptotically quadratic (LAQ) family of statistical experiments. It enables us to make a Bayesian model comparison in a unified manner for a broad range of dependent-data models, thus entailing a far-reaching extension of the classical Schwarz's paradigm with rigorous theoretical foundation. In particular, the proposed quasi-Bayesian information criterion, termed QBIC, prevails even when the corresponding $M$-estimator is of multi-scaling type and the asymptotic quasi-information matrix is random, as well as the statistical model is misspecified. We will illustrate the proposed method by diffusion-type models.

File: 2015-7pdf

Title:Popular Matchings with Ties and Matroid Constraints
Author : Naoyuki Kamiyama
Abstract: In this paper, we consider the popular matching problem with matroid constraints. It is known that if there exists no tie in preference lists of applicants, then this problem can be solved in polynomial time. In this paper, we prove that even if there exist ties in preference lists, this problem can be solved in polynomial time.

File: 2015-6pdf

Title:Existence and stability of time periodic solution to the compressible Navier-Stokes-Korteweg system on $\mathbb{R}^3$
Author : Kazuyuki Tsuda
Abstract: The compressible Navier-Stokes-Korteweg system is considered on $\mathbb{R}^3$ when the external force is periodic in the time variable. The existence of a time periodic solution is proved for a sufficiently small external force by using the time-$T$-map related to the linearized problem around the motionless state with constant density and absolute temperature. The spectral properties of the time-$T$-map is investigated by a potential theoretic method and an energy method in some weighted spaces. The stability of the time periodic solution is proved for sufficiently small initial perturbations. It is also shown that the $L^\infty$ norm of the perturbation decays as time goes to infinity.

File: 2015-5pdf

Title:Large time behavior of solutions to the compressible Navier-Stokes equations around a parallel flow in a cylindrical domain
Author : Reika Aoyama & Yoshiyuki Kagei
Abstract: Stability of parallel flow of the compressible Navier-Stokes equation in a cylindrical domain is studied. It is shown that if the Reynolds and Mach numbers are sufficiently small, then parallel flow is asymptotically stable and the asymptotic leading part of the disturbances is described by a one dimensional viscous Burgers equation.

Nonlinear Analysis Series A: Theory, Methods and Applications , vol.127 (2015), pp. 362--396

Title:Stable Matchings with Ties, Master Preference Lists, and Matroid Constraints
Author : Naoyuki Kamiyama
Abstract: In this paper, we consider a matroid generalization of the hospitals/residents problem with ties and master lists. In this model, the capacity constraints for hospitals are generalized to matroid constraints. By generalizing the algorithms of O'Malley for the hospitals/residents problem with ties and master lists, we give polynomial-time algorithms for deciding whether there exist a super-stable matching and a strongly stable matching in our model, and finding such matchings, if they exist.

Lecture Notes in Computer Science

Title:Spectral properties of the semigroup for the linearized compressible Navier-Stokes equation around a parallel flow in a cylindrical domain
Author : Reika Aoyama & Yoshiyuki Kagei
Abstract: This paper is concerned with the stability of a parallel flow of the compressible Navier-Stokes equation in a cylindrical domain. The spectrum of the linearized operator is analyzed for the purpose of the study of the nonlinear stability. It is shown that if the Reynolds and Mach numbers are sufficiently small, then the linearized semigroup is decomposed into two parts; one behaves like a solution of a one dimensional heat equation as time goes to infinity and the other one decays exponentially. Some estimates related to the spectral projections are established, which will also be useful for the study of the nonlinear problem.

Advances in Differential Equations, vol.21 (2016), no. 3-4, pp. 265--300

Title:Sparse regularization for multivariate linear models for functional data
Author : Hidetoshi Matsui & Yuta Umezu
Abstract: We consider a problem of variable selection in multivariate linear models where the predictors are given as functions and the responses are scalars, with the help of sparse regularization. Observations corresponding to the predictors are supposed to be measured repeatedly at discrete time points, and then they are treated as smooth functional data. Parameters included in the functional multivariate linear model are estimated by the penalized least squared method with the l1/l2-type penalty. We construct a blockwise coordinate descent algorithm for deriving the estimates of the functional multivariate linear model. A tuning parameter which control the degree of the regularization is decided by information criteria. Theoretical properties of our procedure are also presented. In order to investigate the effectiveness of the proposed method we apply it to the analysis of simulated data and real data.

File: 2015-1pdf